Algorithms for Del Pezzo surfaces of degree 5 (construction, parametrization) (Q765865)

A Del Pezzo surface is a complete nonsingular surface such that the anticanonical divisor \(-K\) is ample. The degree \(d\) of the surface is \(K^2\). Del Pezzo surfaces are \(\mathbb{P}^1\times \mathbb{P}^1\) or blowing up of \(\mathbb{P}^2\) at points in general position. Del Pezzo surfaces of degree 5 are parametrizable. An algorithm to compute a parametrization is given. The algorithm is based on a modification of the \textit{N. I. Sheperd--Barron} construction [Bull. Lond. Math. Soc. 24, No. 3, 249--250 (1992; Zbl 0781.14037)]. An algorithm for the construction of examples of Del Pezzo surfaces of degree 5 is given. An algorithm is given to decide the isomorphy of two given quintic Del Pezzo surfaces.